This advanced introductory textbook offers a comprehensive approach to non-relativistic Quantum Mechanics, focusing on exact methods and mathematical techniques often overlooked in standard textbooks. Bridging the gap between foundational concepts and advanced topics, this book introduces numerous methods--some of which are entirely new--making it an invaluable resource for students and researchers alike. Key topics include open quantum systems, entanglement, and supersymmetry, providing a modern perspective on the subject. With eight in-depth chapters, it covers: Quantum Mechanics: A New Paradigm Hilbert Space Formulation of Quantum Physics Schrödinger Equation I Symmetry, Angular Momentum, and Statistics Schrödinger Equation II Path Integrals Quantum Entanglement Methods, Techniques, and Approximation Schemes Perfect for those seeking a deeper understanding of quantum mechanics beyond the basics, this textbook combines theory with practical mathematical methods to present the full scope of the subject's complexity.